Although we assumed the response to be continuous, it is straightforward to incorporate other types of responses in our framework, such as binary or count variables. In particular, we can model the response variables as falling in an exponential family with the linear predictor having exactly the form described earlier in this article. For binary outcomes and assuming a logistic link function, our proposed computational algorithm can be easily modified by relying on Polya-Gamma data augmentation [1]}. A related approach can be used for counts, or our Gibbs steps can be replaced with gradient-based updates to avoid data augmentation. It is additionally straightforward to include further applied complications, such as spatially or temporally dependent data, by incorporating appropriate terms in the linear predictor.
